Determination of the One-to-One Correspondence between the Kinematic Screw of the Output Link and the Gradient Screw in a Singular Configuration of a Parallel Mechanism
Authors: Gebel E.S., Glazunov V.A. | Published: 06.07.2017 |
Published in issue: #7(688)/2017 | |
Category: Calculation and Design of Machinery | |
Keywords: parallel mechanism, Gough–Stewart platform, singularity, Plücker coordinates, kinematic screw, power screw |
The Gough-Stewart platform with six degrees of freedom is widely used in various mechatronic devices, for example, in measuring heads, test benches, etc. It can guarantee high accuracy in controlling the movement and orientation of the output link in the working space as well as the rigidity of the device under dynamic loads. One of the disadvantages of such mechanisms is the possible loss of controllability. A parallel mechanism of the Gough-Stewart platform type is considered. It represents the second class of singularity where the power screws translated from the kinematic chains onto the output link, become linearly dependent and reciprocal to one kinematic screw. Two singular positions of the mechanism are studied in which all points of intersection of the power screws lie on one straight line coinciding with the Ox axis of the stationary Cartesian coordinate system xOy or are arbitrarily located in the plane z = –1. The kinematic screw and the gradient screw that most rapidly exit the singularity are discussed.
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